CH. X TIME CUEVES 221 



wheel the acceleration is 1'5 f.p.s. per second; the final 

 speed is 30 feet per second, M, v, c a , and W, being the 

 same in all cases. 



We here assume that we are dealing with one motor, 

 or that if two motors are used, they are connected in 

 parallel throughout. If there are two motors, connected 

 first in series, and then in parallel, the accelerating current 

 from the line remaining the same throughout, that is, the 

 accelerating current per motor when in series being twice 

 what it is in parallel, the best result is not obtained when 

 half the distance is travelled during acceleration, but when 

 about two-thirds the distance is thus covered. It follows 

 that the best diameter for the series-parallel method of 

 control is rather larger than that for the parallel method, 

 the ratio of the cubes of the diameters being very nearly 

 as the square root of two to one. If then we wish to find 

 the best diameter for the series-parallel method of control, 

 we may substitute 0'834 for O59 in Equation 102. The case 

 when the accelerating current per motor is the same through- 

 out the whole process of acceleration is discussed later on. 



Equation 102 shows that for any value of Mv 

 there is a certain value of d that will cover the given 

 distance in the shortest time. If d be made larger or 

 smaller than this, the time occupied will be increased. 

 We shall find, however, that there is a considerable range 

 of values above and below the best value, for which the 

 time occupied differs but little from the shortest time. 



While the best value of - '? enables us to cover the dis- 



Mv 



tance in the shortest time, it does not do so with the least 



expenditure of energy. The larger the value of ' - the 



Mv 



